Such inertial systems are VERY prone to cumulative velocity and location offset errors due to device offset and ADC/numeric intergrity errors. In general you need to get a position or at least an absolute velocity (wheel tachometers) periodically to correct the error. For example it can be added to a GPS system to provide a more accurate, detailed understanding of your velocity and direction while navigating turns than the periodic GPS coordinates would provide.
I'd think that taking instantaneous readings and doing integration digitally makes more sense. The PIC18F series has a 10 bit ADC. This may not be best for 2 reasons. One, 10 bits may not be enough resolution. Two, accelerometers are differential devices and these 18F ADCs don't do differential directly. It may be simplest to use an external, differential, high resolution ADC.